Question

Estimate the limit.
Picture provided below.

Answer 1

A.
`\lim_(x \to 0) (√(x+2)-√(2))/(x)=0.3535`

Explanation:

We are given the limit expression,
`\lim_(x \to 0) (√(x+2)-√(2))/(x)`

As, we see that,

When
`x\rightarrow 0`, the function is of the form
`(0)/(0)`.

So, we will use L'Hospital's Rule to proceed further i.e. Differentiate the numerator and denominator with respect to x.

That is,

`\lim_(x \to 0) (√(x+2)-√(2))/(x)`

implies
`\lim_(x \to 0) ((1)/(2√(x+2)))/(1)`

i.e.
`\lim_(x \to 0) (1)/(2√(x+2))}=(1)/(2√(2))=0.3535`

Thus,
`\lim_(x \to 0) (√(x+2)-√(2))/(x)=0.3535`

Hence, option A is correct.